In your slow cooker, combine the shredded chicken, cream cheese cubes, sour cream, 1.5 cups of the Monterey Jack cheese, lime juice, tequila, and triple sec.
Add the diced green chiles, lime zest, salt, and cayenne pepper, then stir everything together until well mixed.
Cover and cook on low for 2-3 hours, stirring every hour, until the cheese is completely melted and the dip is hot throughout.
Sprinkle the remaining 1/2 cup cheese on top, cover, and cook for an additional 15 minutes until melted.
Garnish with fresh cilantro and additional lime zest if desired, and serve warm with tortilla chips and lime wedges on the side.